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14. Associative Property for Addition

15. Inverse for Addition

1.3

1. 2

2. −17

3. −54

4. 4

5. 3

6. 14

7. 24

8. −3

9. −8

10. 18

11. 2

12. 7

13. −32

14. −10

15. −40

16. −12

17. −1

18. −48

19. 16

20. 5

1.4

1. 9

2. 225

3. 10

4. 4

5. 23

6. 21

7. 3

8. 15

9. 20

10. −2

1.5

1. 11t

2. 4x

3. 3x + 3y

4. x + 10y − 3

5. −1 + 2x − 2x2

6. 13t − 3r − 10

7. 7x2 − 6x + 19

8. 8x − 6y − 19

9. 2x2 + 2x + 1

10. 10y − 9x

11. 2 + 3x

12. 3y − 7

14. 9n − 8

15. w +(−w)

17. r2 − 4r

19.(3z + 2)(4z − 6)

1.6

1. 14

2. −16

3. 1

4. 2

5. 15

6. 1

7. 85

8. 230

9. −3

10. −26

2 Linear equations

2.1

1. x = 4

2. y = 16

3. t = 3

4. w = 37

5. x = 2

6. z = 13.1

8. x −6

9. y = 3

10. t −7

2.2

1. x = 4

2. z = 63

4. t −36

5. x = 30

6. w = 15.4

8. m −12.4

9. x −3

10. z = 175

2.3

1. x = 13

2. t = −3

3. x = 5

5. x = 12

6. x = 7

7. x = 16

8 x = 0.5

9. x = 25

10. x −8

2.4

1. x = 5

2. x −4

3. 17 = x

4. −1 = x

6. x = 5.8

7. x = 2.5

8. x = 31

2.5

1. x = 6

2. x = 10

3. 11 = x

4. x = 0

5. 11 = x

6. 2 = x

7. x = 6

10. x = 3

2.6

3. x = 9 x = −9.8

4. x = 5 x = −6

5. x = 5.5 x = −7.25

6. x = 2 Reject because it will make the 18x negative,

7. x = 5(Reject x = −10)

8. x = 9.5 x = 0.75

9. x = 4 x = −2

2.7

1. 5 nickels

2. , or 4 h and 10 min, later

3. lb of peanuts and lbs of raisins

4. 30 mg of full strength and 70 mg of 50% solution

5. 5:00 p.m.

6. 250 pennies

7. 481 students

8. oz

9. 1:25 p.m.

10. 2:30 p.m.

3 Linear inequalities

3.1

3.2

3.3

4 Coordinate graphing

4.1

6. Quadrant II

7. Quadrant I

8. Quadrant IV

9. Quadrant III

10. Quadrant IV

4.2

6. a = 4, a = 10

7. d= 15, d = −9

8. c = 15, c = 1

9. b = −10, b = 8

10. a = ±4

4.3

1.(3.5, 5.5)

2.(−2, 4.5)

3.(−3, −2)

4.(4, 4)

5.(2, −3)

6. x = 2

7. x = 7

8. y = 9

9. x = −5

10. x = 16

4.4

3. m = 0

5. Undefined

6. y = −2

7. x = 4

8. y = 4.5

9. x = −8

10. y = 3

4.5

4.6

4.7

1. Vertical

2. Horizontal

3. Vertical

4. Oblique

5. Horizontal

4.8

4.9

4.10

4.11

1. Perpendicular

2. Parallel

3. Neither

4. Parallel

5. Perpendicular

5 Systems of linear equations and inequalities

5.1

5.2

5.3

1. x = 5, y = 5

2. x = 4, y = 8

3. x = 3, y = 9

4. x = 30, y = 27

5. x = 19, y = 23

6. x = 54, y = 8

7. x = 3, y = 1

8. x = 9, y = 4

9. x = 11, y = 2

10. x = −1, y = 5

5.4

1. x = 6, y = 2

2. x = 10, y = 7

3. x = 4, y = 1

4. x = 7, y = 1

6. x = 2, y = 3

7. x = 3, y = 0

8. x = 3, y = 10

9. x = 8, y = −7

5.5

1. a = 1, b = 6

2. x = 1, y = 10

3. x = 2.5, y = −2

4. x = 7, y = 3

5. x = 5, y = 2

5.6

1. Dependent

2. Inconsistent

3. Consistent

4. Inconsistent

5. Dependent

6. Consistent

7. Consistent

8. Inconsistent

9. Consistent

10. Dependent

6 Powers and polynomials

6.1

1. x11

2. y6

3. 6x6

4. 21x10

5. x6

7. y7

9. x2

10. y21

11. x0 = 1

12. x10

13. x2

15. x6

6.2

1. 4x10

2. −8x9

3. 20a8

4. −27x5 y15

5. 72b11

6.3

1. 2x3 + 3x2 + 5x − 7; degree 3

2. 5t12 + t7 + 8t2 − 9t − 1; degree 12

3. −12y11 + 5y6 − 2y3 + 8; degree 11

4. Not a polynomial; variable under radical

5. 2x5 − 4x3 + 3x; degree 5

6. −3z7 − 4z2 + 8z + 4; degree 7

7. w5 − 9w3 − 3w + 7; degree 5

8. −b4 + b2 − 3b − 4; degree 4

9. Not a polynomial; variable in denominator

10. −7y3 + 8y2 − 4y + 6; degree 3

6.4

1. 14w2 − 9w − 1

2. 2a2 − 5a − 4

3. −9x2 + 41x − 24

4. −4y2 − 3y + 32

5. 4 −b + 4b2

6. 4b2 − 3b + 3

7. 11x2 − 13x + 2

8. −2x2− 7x + 2

9. −3x2 + x + 2

10. 2x2 − 16x + 3

6.5

1. −6b7

2. 30x4 y4

3. −36x5 y2 z10

4. −3a2b2c3

5. 40a3b

6. 18x6y3

7. −36w5x6

8. 4x6

9. 20b8

10. −27r3t9

6.6

1. 10a3 + 15a2

2. −2x4 + 6x3 + 4x2

3. 22y4 − 6y3 + 10y2

4. −6b5 + 9b4 − 12b3

5. 3x3 y + 5x2 y2 − 2xy3

6. 25x4 y − 35x3y2 + 5x2 y3

7. 8x2 + 16xy − 24xz

8. −5a3 b + 5ab4

9. 4x10 − 3x8 + 5x7 − x5 + 7x4 − 10x3

10. 9a6b4c2 − 6a4b4c3 + 21a9b3c6

11. 3(x + 1) = 3x + 3

6.7

1. x2 + 10x + 16

2. y2 − 13y + 36

3. t2 + 4t − 12

4. 2x2 + 2x − 24

5. 3y2 − 26y − 9

6. 15x2 + 2x − 24